Heuristics compression

The Lagrangian sound speed is obtained in the following heuristic way. We consider small departures from the shock-compressed state, where the bulk and shear moduli are K and G. The Eulerian sound speed c is then given by... 

We note from Fig. 9 that the individual bonded and nonbonded contributions to t — 22, as they vary with p, are approximately equal in absolute value although opposite in sign. A possible heuristic picture for this behavior is based on Fig (8a) because of the short range and strongly repulsive character of u b, a nonbonded interaction has the character of a classic collision—the duration of an individual interaction is very short. As a result, the impacted atom (fl in Fig. 8a) moves little and the resultant of the impulsive compressive forces in its bonds to oq and a2 balance that exerted by x ( on [>. However, a collision in the configuration shown in Fig. 8b would contribute an impulsive tensile force to its bonds, but a collision between y ( and fi in that configuration is less likely because of steric shielding and, as verified in simulations, occurs less frequently. 

In practice, since we are only interested in an estimate of the effect, we resort to an approximate analysis in which the relevant chemical potentials and mass flux, and attendant strain rate are all evaluated heuristically. The argument begins with reference to fig. 11.6 with the claim that the vacancy formation energy for the faces subjected to tensile stresses differs from that on the faces subjected to compressive stresses. Again, a rigorous analysis of this effect would require a detailed calculation either of the elastic state of the crystal or an appeal to atomistic considerations. We circumvent such an analysis by asserting that the vacancy concentrations are given by... 

The following heuristic should be obvious Do not separate two components and then remix them at a reactor inlet. We must also have in mind the significant difference between the cost of recycling a gas or a liquid. Compressors are very expensive and the cost of compression is very high, whereas the cost of pumping is much lower, except in special applications (viscous liquids, slurries, aggressive solutions, etc). 

In the early 1970s, the Author was in touch with Professor Johannes Muller of the German Democratic Republic. Muller (1970) created systematic heuristics for domestic use in the area of inventive designing. (The Author even wrote a book chapter on the method [Arciszewski 1978].) The name systematic heuristics is a compressed analogy combining two contra-dictive concepts, and obviously such a science could be developed only in a totalitarian society, providing another proof of the impact of environment on creators. 

Note that an alternative flowsheet would place operations 1 and 2 after operation 3. However, this is very uneconomical, as the cost of compressing a vapor is far greater than the cost of pumping a liquid because the molar volume of a vapor is so much greater than that of a liquid (typically, a factor of 100 times greater). For a more complete discussion of this observation, which is just one of many design heuristics or rules of thumb, see Section 5.7. 

Heuristic 35 Estimate the theoretical adiabatic horsepower (THp) for compressing a gas from ... 

Heuristic 36 Estimate the number of gas compression stages, N, from the following table, which assumes a specific heat ratio of 1.4 attd a trutximum compression ratio of 4 for each stage. 

The following heuristic provides an estimate of the theoretical pump Hp. Unlike the case of gas compression, the temperature change across the pump is small and can be neglected. 

Heuristic 43 To increase the pressure of a stream, pump a liquid rather than compress a gas, unless refrigeration is needed. 

Heuristic 51 Particle-size enlargement. Use compression with rotary compression machines to convert powders and granules into tablets of up to 1.5 inches in diameter. Use extruders with cutters to make pellets and wafers from pastes and melts. Use roll compactors to produce sheets from finely divided materials the sheets are then cut into any desired shape. Use rotating drum granulators and rotary disk granulators with binders to produce particles in the size range of 2 to 25 mm. 

How to invent or reuse appropriate predicates How to implement " invented predicates The combination of partial results often is a full-scale problem by itself, as illustrated by the logic algorithms for compress (induction on C), permutation , and sort . The same holds for a decomposition following the Extrinsic Heuristic. This is known as the predicate invention problem. 

Example 12-11 For the compress problem, Step 2 proceeds as follows. At Task A, both parameters are found to be of an inductive type, namely list. If we considered the specification of Figure 4-1, the heuristics would point towards L being the best induction parameter. Without this extended specification knowledge, a non-deterministic selection of an induction parameter among L, C takes place. We... 

The first logic algorithm is based on a singleton clique (originating from compress, W), that is example of. compress)), and is thus subject to generalization by Heuristic 13-1. But there is no property in P(compress) that generalizes 1, so no generalization can be performed here. At Task N, the instance solveCompress/2 is ... 

Example 13-7 For the compress problem, Step 6 proceeds as in Example 10-6. The obtained result is subject to no heuristic. The resulting logic algorithm and its expansion are shown in Example 11-1. 

Example 13-11 For the compress problem. Step 7 proceeds as in Example 9-4. There is one property-example, namely Ej, so Heuristic 13-6 provides E and the properties of EP(compress) as a property-set to the Proofs-as-Programs Method. The applied generalization heuristics are Heuristic 13-3, Heuristic 13-4, and Heuristic 13-5, respectively. The resulting logic algorithm and its expansion are shown in Example 11-1. 

There are thus as many cliques as properties, and Heuristic 13-2 applies. The Synthesis Method is thus invoked. The specification EP(compress) is as in Example 6-1. The logic algorithm LA (compress) will be ... 

---